Hemispherical power asymmetry in the three-year Wilkinson Microwave Anisotropy Probe sky maps

TL;DR

The paper investigates hemispherical power asymmetry in the three-year WMAP CMB data by modeling the sky as an isotropic Gaussian field modulated by a dipole, $f(\hat{n}) = A \hat{n}\cdot \hat{p}$. It uses a Bayesian framework with nested sampling to compute evidence differences $\Delta \log E$ and a frequentist likelihood approach, parameterizing $C_{\ell}$ with $C_{\ell} = q (\ell/\ell_0)^n C_{\ell}^{\text{fid}}$ and exploring $\{q,n,A,\hat{p}\}$ under flat priors. The analysis across Q,V,W, and ILC maps (with foreground marginalization and sky cuts) finds a consistent modulation amplitude $A \sim 0.11$–$0.13$ and a preferred axis around $(l,b) \approx (225^{\circ}, -27^{\circ})$, with substantial but not decisive evidence for modulation ($\Delta \log E \sim 1.5$–$1.8$; frequentist $P \approx 0.99$). The results are robust to data set and sky cut, suggesting a real though not conclusive anomaly that could be illuminated by Planck data and polarization measurements.

Abstract

We consider the issue of hemispherical power asymmetry in the three-year WMAP data, adopting a previously introduced modulation framework. Computing both frequentist probabilities and Bayesian evidences, we find that the model consisiting of an isotropic CMB sky modulated by a dipole field, gives a substantially better fit to the observations than the purely isotropic model, even when accounting for the larger prior volume. For the ILC map, the Bayesian log-evidence difference is ~1.8 in favour of the modulated model, and the raw improvement in maximum log-likelihood is 6.1. The best-fit modulation dipole axis points toward (l,b) = (225 deg,-27 deg), and the modulation amplitude is 0.114, in excellent agreement with the results from the first-year analyses. The frequentist probability of obtaining such a high modulation amplitude in an isotropic universe is ~1%. These results are not sensitive to data set or sky cut. Thus, the statistical evidence for a power asymmetry anomaly is both substantial and robust, although not decisive, for the currently available data. Increased sky coverage through better foreground handling and full-sky and high-sensitivity polarization maps may shed further light on this issue.

Figures (2)

• Figure 1: Posterior distributions for the dipole modulation amplitude, marginalized over direction and CMB power spectrum.
• Figure 2: Posterior distribution for the dipole modulation axis, shown for the ILC map and 36.3% sky cut, and marginalized over power spectrum and amplitude parameters. Grey sky pixels indicate pixels outside the $2\sigma$ confidence region. The dots indicate the axis 1) reported by Eriksen et al. (2004) in white; 2) for the ILC map with a 12.8% sky cut in green; 3) for the $Q$-, $V$-, and $W$-bands in red, blue and yellow, respectively. The axis reported by spergel:2007a coincides with the $W$-band axis.